Question

According to a random sample taken at 12 A.M., body temperatures of healthy adults have a bell-shaped distribution with a mean of 98.08°F and a standard deviation of 0.62°F. Using Chebyshev's theorem, what do we know about the percentage of healthy adults with body temperatures that are within 2 standard deviations of the mean? What are the minimum and maximum possible body temperatures that are within 2 standard deviations of the mean? At least % of healthy adults have body temperatures within 2 standard deviations of 98.08°F. (Round to the nearest percent as needed.) The minimum possible body temperature that is within 2 standard deviations of the mean is F (Round to two decimal places as needed.) The maximum possible body temperature that is within 2 standard deviations of the mean is °F (Round to two decimal places as needed.)

Answer 1

According to Chebyshev's theorem, we know that at least 75% of healthy adults have body temperatures within 2 standard deviations of the mean. The minimum possible body temperature that is within 2 standard deviations of the mean is 96.84°F and the maximum possible body temperature is 99.32°F.

Step-by-step explanation:

In Chebyshev's theorem, we know that for any number k greater than 1, at least 1 - 1/k^2 of the data falls within k standard deviations of the mean.

In this case, we are looking for the percentage of healthy adults with body temperatures that are within 2 standard deviations of the mean. According to Chebyshev's theorem, we know that at least 1 - 1/2^2 = 1 - 1/4 = 75% of the data falls within 2 standard deviations of the mean.

The minimum possible body temperature that is within 2 standard deviations of the mean can be calculated as mean - 2 * standard deviation = 98.08°F - 2 * 0.62°F = 98.08°F - 1.24°F = 96.84°F.

The maximum possible body temperature that is within 2 standard deviations of the mean can be calculated as mean + 2 * standard deviation = 98.08°F + 2 * 0.62°F = 98.08°F + 1.24°F = 99.32°F.

Therefore, at least 75% of healthy adults have body temperatures within 2 standard deviations of 98.08°F. The minimum possible body temperature that is within 2 standard deviations of the mean is 96.84°F and the maximum possible body temperature is 99.32°F.